Question

If the sum of the squares of the zeroes of the polynomials 6x2 + x + k is 25/36, find the value of k?

Answer 1

let alpha and beta be the zeroes of the given polynomial

recall that the sum of polynomial
alpha + beta = -coefficient of x /coefficient of x2=-1/6
product of zeroes of polynomial(alpha beta )= constant term /coefficent of x2


given (alpha2 + beta 2) =25/36
(alpha + beta)2 - 2alpha beta = 25/36

((-1/6))2 -2 k/2 =25/36

1/36 - k/3 = 25/36
1/36 -25/36 = k/3
k/3 = -24/36 =-2/3
k =-2